Question: A circle with circumference $10\pi$ has an arc with a $72^\circ$ central angle. What is the length of the arc? ${10\pi}$ ${72^\circ}$ $\color{#DF0030}{2\pi}$
Solution: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{72^\circ}{360^\circ} = \dfrac{s}{10\pi}$ $\dfrac{1}{5} = \dfrac{s}{10\pi}$ $\dfrac{1}{5} \times 10\pi = s$ $2\pi = s$